Question

An insect, of mass 7 m, is at the bottom of a hemispherical bowl of radius R. The coefficient of friction, between the legs of the insect, and the surface of the bowl, is μ. The insect starts crawling up the hemisphere, but slides down after climbing up a height h above its starting point. The equation, connecting h and R, is

(1) h² -(2R+μ)h + μR = 0

(2) h² + (2R+μ)h - μR = 0

(3) μh² + 2Rh - μR = 0

(4) μh² + (2R + μ)h + μR = 0

Answer 1

(1) h² -(2R+μ)h + μR = 0

The insect can keep on crawling up till the component of its weight, down the bowl, equals the force of limiting friction between the insect and the bowl. 

At the height, h, we then have

N = mg cos α 

and F = force of limiting friction 

= μN = mg sin α